Question

An electron is moving with a kinetic energy of 2.275 x 10^-25J. Calculate its de-Broglie wavelength. (Mass of electron = 9.1 x 10^-31 kg, h = 6.6 x 10^-34 Js)

Answer 1

Kinetic energy of electron,

\(\frac{1}{2}\)mv² = 2.275 x 10^-25 J

or = 2.275 × 10⁻²⁵ kg m² s⁻²

m = 9.1 × 10⁻³¹ kg

v² = \(\frac{2\times2.275\times10^{-25}kg\,m^2s^{-2}}{9.1\times10^{-31}kg}\)

= 0.5 × 10⁶ m² s⁻²

v = 0.7.7 × 10³ ms⁻¹

Now,

\(h=\frac{h}{mv}\)

h = \(\frac{6.6\times10^{-34}kgm^2s^{-1}}{(9.1\times10^{-31kg})\times(0.707\times10^3ms^{-1})}\)

= 1.026 × 10⁻⁶ m = 1026 nm.